多层蒙特卡罗及其在金融工程中的应用
Multilevel Monte Carlo and its Applications in Financial Engineering
摘要：
在这篇文章中，我们提出了一个评论的最新发展主题的多层蒙特卡罗（MLMC）算法，在金融工程中的应用范例。我们特别关注最近在两个子领域进行的研究，即期权定价和金融风险管理。对于前者，讨论涉及结合的重要性抽样算法，与MLMC估计，从而构建一个混合算法，以实现减少的估计的整体方差。在后者的情况下，我们讨论的研究进行，以构建一个有效的算法，以估计风险价值（VaR）和条件方差（CVaR）的风险措施，在一个有效的方式。在这方面，我们简要地讨论了动机和自适应采样算法的建设，目的是有效地估计嵌套的期望，这在一般情况下是计算昂贵的。
英文摘要：
In this article, we present a review of the recent developments on the topic of Multilevel Monte Carlo (MLMC) algorithm, in the paradigm of applications in financial engineering. We specifically focus on the recent studies conducted in two subareas, namely, option pricing and financial risk management. For the former, the discussion involves incorporation of the importance sampling algorithm, in conjunction with the MLMC estimator, thereby constructing a hybrid algorithm in order to achieve reduction for the overall variance of the estimator. In case of the latter, we discuss the studies carried out in order to construct an efficient algorithm in order to estimate the risk measures of Value-at-Risk (VaR) and Conditional Var (CVaR), in an efficient manner. In this regard, we briefly discuss the motivation and the construction of an adaptive sampling algorithm with an aim to efficiently estimate the nested expectation, which, in general is computationally expensive.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
